Substitution and Elimination

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is elimination in solving systems of equations?

Back

Elimination is a method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve for x and y: 2x − 3y = −1, y = x − 1

Back

(4, 3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations: 3x + 2y = 16, 14x + 2y = 38?

Back

(2, 5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system: x + y = 19, y = 3x - 1

Back

(5, 14)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, as the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

Solve for x and y: 4x + 8y = 20, -4x + 2y = -30

Back

(7, -1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6